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Hydraulic accumulator with spring used for energy storage

Accumulators

## Description

This block represents a spring-loaded accumulator, where fluid entering the accumulator compresses the spring, thus storing hydraulic energy. Since the spring compression increases as fluid enters the chamber and decreases as the accumulator is discharged, the pressure is not constant. The spring is preloaded. If the fluid pressure at the accumulator inlet becomes higher than the preload pressure, fluid enters the accumulator chamber and compresses the spring, thus storing hydraulic energy. A drop in the fluid pressure at the inlet forces the stored fluid back into the system.

To improve computational convergence and efficiency, the accumulator shell is assumed to be compliant. As a result, the fluid starts accumulating in the chamber even before the preload pressure is reached, so that at preload pressure the accumulator already stores a certain volume of fluid. The structural compliance can be set to a very small value, but not to zero.

The accumulator is described with the following equations:

where

 p Pressure at the accumulator inlet q Flow rate into accumulator Vmax Accumulator capacity (maximum volume) VF Instantaneous volume of fluid in the accumulator Vpr Volume of fluid at preload pressure ppr Preload pressure pmax Pressure needed to fully fill the accumulator Ks Structural compliance of the accumulator shell k Gain coefficient

The block positive direction is from port A into the accumulator. This means that the flow rate is positive if it flows into the accumulator.

## Basic Assumptions and Limitations

• The spring has linear characteristics.

• No loading on the separator, such as inertia, friction, and so on, is considered.

• Fluid compressibility is not taken into account.

## Dialog Box and Parameters

Capacity

Accumulator volumetric capacity. The default value is 0.008 m^3.

Pressure at which fluid starts entering the chamber. The default value is 1e6 Pa.

Maximum pressure

Pressure at which the accumulator is fully charged. The default value is 3e6 Pa.

Initial fluid volume

Initial volume of fluid in the accumulator. This parameter specifies the initial condition for use in computing the block's initial state at the beginning of a simulation run. For more information, see Initial Conditions Computation. The default value is 0.

Structural compliance

The compliance of the accumulator shell. This parameter is introduced to improve convergence and computational efficiency. It must be greater than zero. Values less than 1e-16 m^3/Pa may result in numerical instability. The default value is 4e-15 m^3/Pa.

## Ports

The block has one hydraulic conserving port associated with the accumulator inlet.

The flow rate is positive if fluid flows into the accumulator.